Neutron scattering measurements of the phonon density of states of ${\text{FeSe}}_{1-x}$ superconductors

Inelastic neutron-scattering experiments have been carried out on polycrystalline samples of the ${\text{FeSe}}_{1-x}$ superconductors. We report the phonon density of states for ${\text{FeSe}}_{1-x}$ with $T_c\approx 8\text{K}$. The phonon cutoff frequency is observed around 40 meV. No significant change is observed across the superconducting transition. The measurements support the published first-principles calculations [A. Subedi et al., Phys. Rev. B 78, 134514 (2008)].

Figure 1

(Color online) (a) X-ray diffraction patterns of samples A and B. Reflections are labeled in tetragonal $\left(P4/nmm\right)$ notation. Positions of possible impurity peaks (very weak) are denoted with the symbols $\beta ,\ast ,$ and $\nabla$, for $\beta \text{-FeSe}$, ${\text{Fe}}_3{\text{O}}_4$, and ${\text{Fe}}_3\text{Si}/\text{Fe}$, respectively. (b) Electrical resistivity of sample B.

Figure 2

(Color online) Observed (red $+$) and fitted (solid green) powder neutron-diffraction pattern of sample B as measured on BT-1 at (a) $T=298\text{K}$ and (b) $T=4\text{K}$. The regions of missing data are masked and correspond to aluminum reflections. The difference curve is shown at the bottom in solid black and the calculated positions of the reflections are shown. The insets show the clear splitting of reflections at 6 K and indicate the lower symmetry of the low-temperature phase. The inclusion of a weak NiAs phase of FeSe was included to slightly improve the fits.

Figure 3

(Color online) (a) The measured PDOS of sample A at 3.8 K. Data taken with the PG (002) monochromator is shown in red, whereas data taken with the Cu (220) monochromator is shown in blue. The empty can background has been subtracted from both measurements. The Cu data is multiplied by a constant term to put the same data on the scale with the PG data. The reason that there is a larger dip in the Cu intensity than the PG intensity around 35 meV is that the energy resolution of the Cu monochromator is superior at that energy transfer to that of the PG monochromator. The three peaks below 10 meV are marked for their $\frac{\lambda }{2}$ contamination. (b) The partial PDOS of Fe and Se and the total PDOS, as described in the text. The error bars in (a) and later figures represent the $\pm 1\sigma$ statistical uncertainty.

Figure 4

(Color online) (a) $I\left(\hslash \omega \right)$, in (a), and $I\left(q\right)$, in (b), for sample A at $T=1.5$, 100, 200, and 300 K. $I\left(Q,\hslash \omega =0\right)$, i.e., the diffraction pattern, has been scaled down and is shown at the bottom. The particularly strong Bragg reflection at $Q=3.1{\text{Å}}^{-1}$ is marked with an asterisk for its contamination from the Al sample can and also $\text{Fe}/{\text{Fe}}_3\text{Si}$ impurities. (c) The expected inelastic-scattering spectrum based on the PDOS calculation.

Figure 5

(Color online) A comparison of the measured PDOS of sample A at 3.8 and 13 K and sample B at 3.8 and 100 K. Data are intentionally offset for clarity.